The Barut-Girardello, Klauder-Perelomov and Gazeau-Klauder coherent states for the pseudoharmonic oscillator are constructed and some of their properties are examinated. The diagonal P-representation of the density operator is deduced and the thermal expectation values for a quantum canonical ideal gas of pseudoharmonic oscillators is calculated.

The Barut-Girardello, Klauder-Perelomov and Gazeau-Klauder coherent states for the pseudoharmonic oscillator are constructed and some of their properties are examinated. The diagonal P-representation of the density operator is deduced and the thermal expectation values for a quantum canonical ideal gas of pseudoharmonic oscillators is calculated.

The Barut-Girardello, Klauder-Perelomov and Gazeau-Klauder coherent states for the pseudoharmonic oscillator are constructed and some of their properties are examinated. The diagonal P-representation of the density operator is deduced and the thermal expectation values for a quantum canonical ideal gas of pseudoharmonic oscillators is calculated.

In the present paper we have examined some aspects of the pseudoharmonical oscillators quantum gas. After the deduction of the density matrix expression and the partition function, we have calculated some characteristics of this gas:thermal moments of coordinate, internal energy, free energy, entropy and heat capacity. We have verified the obtained results by passing to the harmonic limit.

For the pseudoharmonical oscillator we have built the creation and annihilation operators and the corresponding coherent states. After the deduction of the density operator expression in coherent-state rep- resentation in two ways (by their definition and by solving the Bloch equation), we have calculated the expected values of some character- istical physical observables.

In the present paper we have extended the quantum virial and Hellmann-Feynman theorems to the quantum statistical averages, i.e. to the thermal states. We have obtained some new formulae which make possible to expressing the thermodinamical observables of the system as functions of the moments of coordinate, as we see in a short example relating to the pseudoharmonical oscillator.

In this paper we have extended the uncertainty relations to mixed states for some special cases of quantum oscillators, relations which are calculated for this kind of states by means of the earlier established virial and Hellmann-Feynman theorems. The lower bound of these uncertainty relations is estimated for a few exactly solvable potentials, too.

In the present paper we have constructed the Green's function for the pseudoharmonical potential, which is considered as an intermediate potential between the harmonic and anharmonic potentials. We have used a hybrid method, by combining the Laplace transformation method and the Green's function technique. The Green's function is used for obtaining the density matrix for a quantum-statistical system, in coordinate representation. Even if this is

A method is presented for solving the Bloch equation for Morse potential, based on the application of Fourier transformation of the density matrix. The results obtained agree completely with the results obtained by other methods, however its advantage lies in its elegance and intuitivity of the approach.